Recurrence of non-resonant homeomorphisms on the torus
Dynamical Systems
2011-05-04 v2
Abstract
We prove that a homeomorphism of the torus homotopic to the identity whose rotation set is reduced to a single totally irrational vector is chain-recurrent. In fact, we show that pseudo-orbits can be chosen with a small number of jumps, in particular, that the nonwandering set is weakly transitive. We give an example showing that the nonwandering set of such a homeomorphism may not be transitive.
Cite
@article{arxiv.1103.4576,
title = {Recurrence of non-resonant homeomorphisms on the torus},
author = {Rafael Potrie},
journal= {arXiv preprint arXiv:1103.4576},
year = {2011}
}
Comments
11 pages. Some corrections made